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受欢迎的三角函数 >

tan(3B+5)=cot(2B+10)

解答

tan (3 B + 5^{\circ}) = cot (2 B + 1 0^{\circ})

解答

B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}, B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

+1

弧度

B = \frac{π}{12} + \frac{2 π}{5} n, B = \frac{17 π}{60} + \frac{2 π}{5} n

求解步骤

tan (3 B + 5^{\circ}) = cot (2 B + 1 0^{\circ})

两边减去

cot (2 B + 1 0^{\circ})

tan (3 B + 5^{\circ}) - cot (2 B + 1 0^{\circ}) = 0

化简

tan (3 B + 5^{\circ}) - cot (2 B + 1 0^{\circ}) : tan (\frac{108 B + 18 0 ^{\circ}}{36}) - cot (\frac{36 B + 18 0 ^{\circ}}{18})

tan (3 B + 5^{\circ}) - cot (2 B + 1 0^{\circ})

化简

3 B + 5^{\circ} : \frac{108 B + 18 0 ^{\circ}}{36}

3 B + 5^{\circ}

将项转换为分式:

3 B = \frac{3 B 36}{36}

= \frac{3 B \cdot 36}{36} + 5^{\circ}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 B \cdot 36 + 18 0 ^{\circ}}{36}

数字相乘:

3 \cdot 36 = 108

= \frac{108 B + 18 0 ^{\circ}}{36}

= tan (\frac{108 B + 18 0 ^{\circ}}{36}) - cot (2 B + 1 0^{\circ})

化简

2 B + 1 0^{\circ} : \frac{36 B + 18 0 ^{\circ}}{18}

2 B + 1 0^{\circ}

将项转换为分式:

2 B = \frac{2 B 18}{18}

= \frac{2 B \cdot 18}{18} + 1 0^{\circ}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 B \cdot 18 + 18 0 ^{\circ}}{18}

数字相乘:

2 \cdot 18 = 36

= \frac{36 B + 18 0 ^{\circ}}{18}

= tan (\frac{108 B + 18 0 ^{\circ}}{36}) - cot (\frac{36 B + 18 0 ^{\circ}}{18})

tan (\frac{108 B + 18 0 ^{\circ}}{36}) - cot (\frac{36 B + 18 0 ^{\circ}}{18}) = 0

用 sin, cos 表示

- cot (\frac{18 0 ^{\circ} + 36 B}{18}) + tan (\frac{18 0 ^{\circ} + 108 B}{36})

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= - \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} + tan (\frac{18 0 ^{\circ} + 108 B}{36})

使用基本三角恒等式:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} + \frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} )}

化简

- \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} + \frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} )} : \frac{- cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} ) + sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}{sin ( \frac{36 B + 18 0 ^{\circ}}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}

- \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} + \frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} )}

sin (\frac{18 0 ^{\circ} + 36 B}{18}), cos (\frac{18 0 ^{\circ} + 108 B}{36})

的最小公倍数:

sin (\frac{36 B + 18 0 ^{\circ}}{18}) cos (\frac{108 B + 18 0 ^{\circ}}{36})

sin (\frac{18 0 ^{\circ} + 36 B}{18}), cos (\frac{18 0 ^{\circ} + 108 B}{36})

最小公倍数 (LCM)

计算出由出现在

sin (\frac{18 0 ^{\circ} + 36 B}{18})

或

cos (\frac{18 0 ^{\circ} + 108 B}{36})

中的因子组成的表达式

= sin (\frac{36 B + 18 0 ^{\circ}}{18}) cos (\frac{108 B + 18 0 ^{\circ}}{36})

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

sin (\frac{36 B + 18 0 ^{\circ}}{18}) cos (\frac{108 B + 18 0 ^{\circ}}{36})

对于

\frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} :

将分母和分子乘以

cos (\frac{108 B + 18 0 ^{\circ}}{36})

\frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} = \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}

对于

\frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} )} :

将分母和分子乘以

sin (\frac{36 B + 18 0 ^{\circ}}{18})

\frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} )} = \frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}

= - \frac{cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}{sin ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )} + \frac{sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} ) + sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}{sin ( \frac{36 B + 18 0 ^{\circ}}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}

= \frac{- cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} ) + sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{36 B + 18 0 ^{\circ}}{18} )}{sin ( \frac{36 B + 18 0 ^{\circ}}{18} ) cos ( \frac{108 B + 18 0 ^{\circ}}{36} )}

\frac{- cos ( \frac{18 0 ^{\circ} + 108 B}{36} ) cos ( \frac{18 0 ^{\circ} + 36 B}{18} ) + sin ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{18 0 ^{\circ} + 36 B}{18} )}{cos ( \frac{18 0 ^{\circ} + 108 B}{36} ) sin ( \frac{18 0 ^{\circ} + 36 B}{18} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- cos (\frac{18 0 ^{\circ} + 108 B}{36}) cos (\frac{18 0 ^{\circ} + 36 B}{18}) + sin (\frac{18 0 ^{\circ} + 108 B}{36}) sin (\frac{18 0 ^{\circ} + 36 B}{18}) = 0

使用三角恒等式改写

- cos (\frac{18 0 ^{\circ} + 108 B}{36}) cos (\frac{18 0 ^{\circ} + 36 B}{18}) + sin (\frac{18 0 ^{\circ} + 108 B}{36}) sin (\frac{18 0 ^{\circ} + 36 B}{18})

使用角和恒等式:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

- cos (s) cos (t) + sin (s) sin (t) = - cos (s + t)

= - cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18})

- cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18}) = 0

两边除以

- 1

- cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18}) = 0

两边除以

- 1

\frac{- cos ( \frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} )}{- 1} = \frac{0}{- 1}

化简

cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18}) = 0

cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18}) = 0

cos (\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18}) = 0

的通解

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 9 0^{\circ} + 36 0^{\circ} n, \frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 27 0^{\circ} + 36 0^{\circ} n

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 9 0^{\circ} + 36 0^{\circ} n, \frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 27 0^{\circ} + 36 0^{\circ} n

解

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 9 0^{\circ} + 36 0^{\circ} n : B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 9 0^{\circ} + 36 0^{\circ} n

乘以最小公倍数

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 9 0^{\circ} + 36 0^{\circ} n

找到

36, 18, 2

的最小公倍数:

36

36, 18, 2

最小公倍数 (LCM)

36

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3

36

36

除以

236 = 18 \cdot 2

= 2 \cdot 18

18

除以

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

计算出由至少在以下一个数字中出现的因数组成的数字:

36, 18, 2

= 2 \cdot 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 = 36

= 36

乘以最小公倍数=

36

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 + \frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 = 9 0^{\circ} \cdot 36 + 36 0^{\circ} n \cdot 36

化简

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 + \frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 = 9 0^{\circ} \cdot 36 + 36 0^{\circ} n \cdot 36

化简

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 : 18 0^{\circ} + 108 B

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 18 0 ^{\circ} + 108 B ) \cdot 36}{36}

约分:

36

= 18 0^{\circ} + 108 B

化简

\frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 : 2 (36 B + 18 0^{\circ})

\frac{18 0 ^{\circ} + 36 B}{18} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 18 0 ^{\circ} + 36 B ) \cdot 36}{18}

数字相除:

\frac{36}{18} = 2

= 2 (36 B + 18 0^{\circ})

化简

9 0^{\circ} \cdot 36 : 324 0^{\circ}

9 0^{\circ} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 324 0^{\circ}

数字相除:

\frac{36}{2} = 18

= 324 0^{\circ}

化简

36 0^{\circ} n \cdot 36 : 1296 0^{\circ} n

36 0^{\circ} n \cdot 36

数字相乘:

2 \cdot 36 = 72

= 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 324 0^{\circ} + 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 324 0^{\circ} + 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 324 0^{\circ} + 1296 0^{\circ} n

展开

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) : 180 B + 54 0^{\circ}

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ})

乘开

2 (36 B + 18 0^{\circ}) : 72 B + 36 0^{\circ}

2 (36 B + 18 0^{\circ})

使用分配律:

a (b + c) = ab + a c

a = 2, b = 36 B, c = 18 0^{\circ}

= 2 \cdot 36 B + 36 0^{\circ}

数字相乘:

2 \cdot 36 = 72

= 72 B + 36 0^{\circ}

= 18 0^{\circ} + 108 B + 72 B + 36 0^{\circ}

化简

18 0^{\circ} + 108 B + 72 B + 36 0^{\circ} : 180 B + 54 0^{\circ}

18 0^{\circ} + 108 B + 72 B + 36 0^{\circ}

对同类项分组

= 108 B + 72 B + 18 0^{\circ} + 36 0^{\circ}

同类项相加:

108 B + 72 B = 180 B

= 180 B + 18 0^{\circ} + 36 0^{\circ}

同类项相加:

18 0^{\circ} + 36 0^{\circ} = 54 0^{\circ}

= 180 B + 54 0^{\circ}

= 180 B + 54 0^{\circ}

180 B + 54 0^{\circ} = 324 0^{\circ} + 1296 0^{\circ} n

将

54 0^{\circ}

到右边

180 B + 54 0^{\circ} = 324 0^{\circ} + 1296 0^{\circ} n

两边减去

54 0^{\circ}

180 B + 54 0^{\circ} - 54 0^{\circ} = 324 0^{\circ} + 1296 0^{\circ} n - 54 0^{\circ}

化简

180 B = 270 0^{\circ} + 1296 0^{\circ} n

180 B = 270 0^{\circ} + 1296 0^{\circ} n

两边除以

180

180 B = 270 0^{\circ} + 1296 0^{\circ} n

两边除以

180

\frac{180 B}{180} = 1 5^{\circ} + \frac{1296 0 ^{\circ} n}{180}

化简

\frac{180 B}{180} = 1 5^{\circ} + \frac{1296 0 ^{\circ} n}{180}

化简

\frac{180 B}{180} : B

\frac{180 B}{180}

数字相除:

\frac{180}{180} = 1

= B

化简

1 5^{\circ} + \frac{1296 0 ^{\circ} n}{180} : 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

1 5^{\circ} + \frac{1296 0 ^{\circ} n}{180}

消掉

1 5^{\circ} : 1 5^{\circ}

1 5^{\circ}

约分:

15

= 1 5^{\circ}

= 1 5^{\circ} + \frac{1296 0 ^{\circ} n}{180}

消掉

\frac{1296 0 ^{\circ} n}{180} : \frac{36 0 ^{\circ} n}{5}

\frac{1296 0 ^{\circ} n}{180}

约分:

36

= \frac{36 0 ^{\circ} n}{5}

= 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}

解

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 27 0^{\circ} + 36 0^{\circ} n : B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 27 0^{\circ} + 36 0^{\circ} n

乘以最小公倍数

\frac{18 0 ^{\circ} + 108 B}{36} + \frac{18 0 ^{\circ} + 36 B}{18} = 27 0^{\circ} + 36 0^{\circ} n

找到

36, 18, 2

的最小公倍数:

36

36, 18, 2

最小公倍数 (LCM)

36

质因数分解:

2 \cdot 2 \cdot 3 \cdot 3

36

36

除以

236 = 18 \cdot 2

= 2 \cdot 18

18

除以

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 3 \cdot 3

18

质因数分解:

2 \cdot 3 \cdot 3

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

计算出由至少在以下一个数字中出现的因数组成的数字:

36, 18, 2

= 2 \cdot 2 \cdot 3 \cdot 3

数字相乘:

2 \cdot 2 \cdot 3 \cdot 3 = 36

= 36

乘以最小公倍数=

36

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 + \frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 = 27 0^{\circ} \cdot 36 + 36 0^{\circ} n \cdot 36

化简

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 + \frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 = 27 0^{\circ} \cdot 36 + 36 0^{\circ} n \cdot 36

化简

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36 : 18 0^{\circ} + 108 B

\frac{18 0 ^{\circ} + 108 B}{36} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 18 0 ^{\circ} + 108 B ) \cdot 36}{36}

约分:

36

= 18 0^{\circ} + 108 B

化简

\frac{18 0 ^{\circ} + 36 B}{18} \cdot 36 : 2 (36 B + 18 0^{\circ})

\frac{18 0 ^{\circ} + 36 B}{18} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 18 0 ^{\circ} + 36 B ) \cdot 36}{18}

数字相除:

\frac{36}{18} = 2

= 2 (36 B + 18 0^{\circ})

化简

27 0^{\circ} \cdot 36 : 972 0^{\circ}

27 0^{\circ} \cdot 36

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 972 0^{\circ}

数字相乘:

3 \cdot 36 = 108

= 972 0^{\circ}

数字相除:

\frac{108}{2} = 54

= 972 0^{\circ}

化简

36 0^{\circ} n \cdot 36 : 1296 0^{\circ} n

36 0^{\circ} n \cdot 36

数字相乘:

2 \cdot 36 = 72

= 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 972 0^{\circ} + 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 972 0^{\circ} + 1296 0^{\circ} n

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) = 972 0^{\circ} + 1296 0^{\circ} n

展开

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ}) : 180 B + 54 0^{\circ}

18 0^{\circ} + 108 B + 2 (36 B + 18 0^{\circ})

乘开

2 (36 B + 18 0^{\circ}) : 72 B + 36 0^{\circ}

2 (36 B + 18 0^{\circ})

使用分配律:

a (b + c) = ab + a c

a = 2, b = 36 B, c = 18 0^{\circ}

= 2 \cdot 36 B + 36 0^{\circ}

数字相乘:

2 \cdot 36 = 72

= 72 B + 36 0^{\circ}

= 18 0^{\circ} + 108 B + 72 B + 36 0^{\circ}

化简

18 0^{\circ} + 108 B + 72 B + 36 0^{\circ} : 180 B + 54 0^{\circ}

18 0^{\circ} + 108 B + 72 B + 36 0^{\circ}

对同类项分组

= 108 B + 72 B + 18 0^{\circ} + 36 0^{\circ}

同类项相加:

108 B + 72 B = 180 B

= 180 B + 18 0^{\circ} + 36 0^{\circ}

同类项相加:

18 0^{\circ} + 36 0^{\circ} = 54 0^{\circ}

= 180 B + 54 0^{\circ}

= 180 B + 54 0^{\circ}

180 B + 54 0^{\circ} = 972 0^{\circ} + 1296 0^{\circ} n

将

54 0^{\circ}

到右边

180 B + 54 0^{\circ} = 972 0^{\circ} + 1296 0^{\circ} n

两边减去

54 0^{\circ}

180 B + 54 0^{\circ} - 54 0^{\circ} = 972 0^{\circ} + 1296 0^{\circ} n - 54 0^{\circ}

化简

180 B = 918 0^{\circ} + 1296 0^{\circ} n

180 B = 918 0^{\circ} + 1296 0^{\circ} n

两边除以

180

180 B = 918 0^{\circ} + 1296 0^{\circ} n

两边除以

180

\frac{180 B}{180} = 5 1^{\circ} + \frac{1296 0 ^{\circ} n}{180}

化简

\frac{180 B}{180} = 5 1^{\circ} + \frac{1296 0 ^{\circ} n}{180}

化简

\frac{180 B}{180} : B

\frac{180 B}{180}

数字相除:

\frac{180}{180} = 1

= B

化简

5 1^{\circ} + \frac{1296 0 ^{\circ} n}{180} : 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

5 1^{\circ} + \frac{1296 0 ^{\circ} n}{180}

消掉

5 1^{\circ} : 5 1^{\circ}

5 1^{\circ}

约分:

3

= 5 1^{\circ}

= 5 1^{\circ} + \frac{1296 0 ^{\circ} n}{180}

消掉

\frac{1296 0 ^{\circ} n}{180} : \frac{36 0 ^{\circ} n}{5}

\frac{1296 0 ^{\circ} n}{180}

约分:

36

= \frac{36 0 ^{\circ} n}{5}

= 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

B = 1 5^{\circ} + \frac{36 0 ^{\circ} n}{5}, B = 5 1^{\circ} + \frac{36 0 ^{\circ} n}{5}

作图

流行的例子

2cot(x)cos(x)+7=7csc(x)

2 cot (x) cos (x) + 7 = 7 csc (x)

2cos(2x-pi/3)=1

2 cos (2 x - \frac{π}{3}) = 1

cos(2θ)= 1/(sqrt(2))

cos (2 θ) = \frac{1}{2}

1 + 4 sin^{2} (θ) = 2

arcsin(x)-arctan(sqrt(3))=-pi/6

arcsin (x) - arctan (3) = - \frac{π}{6}